# The relationship between multiplication and division

### Grade 3: Relating Multiplication and Division: Overview

This is a complete lesson with teaching and exercises about the relationship between multiplication and division, meant for third grade. Students write multiplication and division sentences from the same picture. Lastly, students use their knowledge of multiplication facts to solve. In this chapter your students will learn how to use arrays to show the relationship between multiplication and division. Students will learn that division can be. Free worksheets, online interactive activities and other resources to support children learning the relationship between multiplication and division.

The product is the answer when two or more numbers are multiplied together.

Provide a simple multiplication and division problem using the same numbers. Model how you can change a division problem into a multiplication problem to make the division problem easier to solve.

**multiplication and division as inverse operations**

Highlight that converting multiplication equations to division equations is a strategy to divide by focusing on memorized or familiar multiplication facts. Check your answer using the picture representation of your choice e. Conduct a multiplication fluency game in which there are two teams placed in two lines perpendicular to the board. Project the Division Facts to with One-Digit Divisors exercise and have one student from each team compete to quickly convert the division equation to a multiplication problem and provide the answer.

The students who get the correct answer first win a point for their team. Allow them to use whiteboards as necessary.

### Relating division to multiplication (video) | Khan Academy

Independent working time 10 minutes Distribute the Multiplication and Division Review worksheet and ask students to complete the top section on their own. Allow students to meet in partners to share their answers and correct misconceptions.

Choose students to share any corrections they made and their process to get the right answer with the class. Provide a pre-lesson with simple multiplication and division problems with manipulatives and a review of vocabulary terms and their meanings.

Allow students to practice converting equations with a common factor e. Use a worksheet like the optional Division Facts: A farmer is filling baskets of apples. The farmer has 24 apples and 4 baskets.

## Smartick - Math, one click away

If she divides them equally, how many apples will she put in each basket? When you divide to find the number of groups, the division is called measuring or repeated subtraction. It is easy to see that you can keep subtracting 4 from 24 until you reach zero. Each 4 you subtract is a group or basket. A farmer has 24 apples.

## Division and Multiplication Relationship

How many baskets of 4 can she fill? Manipulatives and visual aids are important when teaching multiplication and division.

Students have used arrays to illustrate the multiplication process. Arrays can also illustrate division.

### Inverse Relationship between Multiplication and Division

Since division is the inverse, or opposite, of multiplication, you can use arrays to help students understand how multiplication and division are related. If in multiplication we find the product of two factors, in division we find the missing factor if the other factor and the product are known. In the multiplication model below, you multiply to find the number of counters in all.

In the division model you divide to find the number of counters in each group. The same three numbers are used.